Question

Is it possible for two numbers to have HCF as $12$ and LCM as $350$?

Answer 1

x & y are the two no.

then, x=12a and y=12b

a,b are relatively prime

Now, 12ab=350

$ab=\frac{3\sqrt{30}}{12}=\frac{175}{6}$

$\therefore$ a & b $\Rightarrow (\frac{25}{6},7)(\frac{7}{6},25)(\frac{7}{3},\frac{25}{2})(\frac{7}{2},\frac{25}{3})$

$\therefore x$ & $y\Rightarrow (50,84)(14,300)(28,150)(42,100)$